含损伤粘弹性本构及其在有限元分析中的实现

Viscoelastic Constitutive Model with Damage Evolution and Its Implementation in Finite Element Analysis

为研究固体发动机药柱的损伤粘弹性行为,针对一种耦合损伤的三维非线性粘弹性本构模型,采用积分算法对其进行了数值离散,导出了本构方程的增量有限元形式。针对该增量型本构方程对应的非线性方程组,建立了采用Newton-Raphson迭代法求解的应力更新方法,并基于Abaqus软件和Fortran语言开发了相应材料本构子程序,最后应用算例对所设计数值方法及程序进行了验证与分析。结果表明,本文有限元解与对应解析解吻合良好,保持了很高的精度,所设计方法及程序有效,可应用于实际型号发动机药柱损伤结构分析。

For the purpose of analyzing the nonlinear viscoelasticity with damage for solid rocket motor（SRM） grain,based on a 3-D nonlinear viscoelastic constitutive model with damage evolution,the incremental finite element form was derived with numerical integral arithmetic and the stress updating methods were presented in an increment according to numerical iteration methods of Newton-Raphson by solving these nonlinear equations.The corresponding material subroutine was developed with Fortran code based on secondary development of Abaqus software.Moreover,the present numerical method and subroutine were verified through analytical solutions of typical examples.Cases study indicates that the finite element solutions with material subroutine is in good agreement with the analytical ones and keeps high accuracy.The methods and subroutine,which have been proved to be of validity in this study,may be applied to structural analysis for practical SRM grain.